State Observer and Controller Design for an Inverted Pendulum on a Cart 
Q1. What are the Eigen values of the system matrix 
?
?
Q2. What is the state feedback gain matrix 
for the 
and desired poles 
?
for the and desired poles ?
Q3. What is the state feedback gain matrix for the given 
and the desired characteristic equation 
?
for the given and the desired characteristic equation ?
Q4. What is the observer gain matrix 
for the given system 
and desired poles are 
?
for the given system and desired poles are ?
Q5. What is the characteristic equation of the state observer?